There's been a bit of talk on this recently and after removing my badge this morning, I thought it made sense to make a How-To. If anyone has any other methods feel free to post here, and if mods think this isn't worth a topic then feel free to remove
I think all BMW's except for the 'M' models look better without a badge such as '318' , '320d' etc (in my case '318 is'). I removed the badge on my old E36 and I've also removed badges on other cars such as my old Fiesta.
The method below is just a method I've used with good results and no marks leftover, but others may post their methods
Rear model badge removal
1) Get a hairdryer and blow on hottest setting over badge thoroughly for about 5 minutes, ensuring its 'ouch' hot when you touch it.
2) Get some dental floss and pull it down behind the badge to loosen it
3) Get an old credit card and slide it down the back of the badge and ease it off, it will need a little pressure. If its too difficult without force at this stage, heat it up further with the hairdryer.
4) Once the metal part of the badge is off, there might be some adhesive still on the car. Don't worry at this point.
5) Wash with warm water over the area where the badge was and then heat it with the hairdryer again.
6) The adhesive should now peel off easily, again if it doesn't apply more hot air.
7) Once the adhesive is off, clean the area again with warm water.
8) Apply AutoGlym's "Intensive Tar Remover" or equivalent generously to the area and leave to dry for a couple of minutes.
9) Wash area with water again and leave to dry and the rear of your car should be clear of badge, adhesive and scratches
10) Wash rest of the car, at least the rear of the car so there's not just a certain clean area on the rear of the car. Just what I noticed as the rest of the back of my car was filthy